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This monthly journal, begun in 1950, is devoted entirely to research in
pure and applied mathematics, principally to the publication of original
papers of moderate length. A section called Shorter Notes was established
to publish very short papers of unusually elegant and polished character
for which there is normally no other outlet.

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Abstract

In [2], Golod, using results of Golod and Shafarevich [1], has constructed a finitely generated algebra $A = K\langle y_1,\ldots, y_d \rangle$, over any field K, such that the ideal generated by y1,..., yd is nil, but dimK A = ∞. Moreover, when $\operatorname{char} K = p > 0$, the subgroup G of the group of units of A, generated by 1 + y1,..., 1 + yd, is an infinite p-group. The main purpose of the present paper is to show that K[ G ], the group algebra of G over K, is not isomorphic to A for "most" Golod-Shafarevich groups G.